Mixtures & Alligations Question Answers

Mixtures and Alligations - Quant/Math - CAT 2008

Question 4 the day: August 19, 2002
The question for the day is from the topic of Mixtures and Alligations.

A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?

(1)

1 kg

(2)

5 kgs

(3)

3 kgs

(4)

6 kgs

Correct Answer - (2)

 

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Solution:

If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg.

We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg.
Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C.
Step 1: Find out the ratio QA : QC using alligation rule.  Qa / Qc  = 30-25  /  25-20  =1/1
Step 2: Find out the ratio QB : QC using alligation rule.   Qb / Qc  = 30-25  /  25-24  =5/1
Step 3: QC is found by adding the value of QC in step 1 and step 2 = 1 + 1 = 2
Therefore, the required ratio = 1 : 5 : 2
If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture.

Note: This is a problem to be skipped, at least in the first go. If you were able to solve at least 30 other problems in quant, then you should look at this problem.